I think it is this you're looking for?

PV = nRT

Where P is pressure. V is volume. T is temperature (Kelvin). R is the universal gas constant (8.3145 J/mol K) and n is the number of moles of gas molecules (mole volume).

To calculate the pressure, calculate the number of moles n in your gas.

Multiply that by R, multiply by temperature, divide by volume.

You don't need the surface area, but you need to know the volume.

Knowing the mass of the gas you can divide it by the molar mass.

Knowing the number of molecules you can divide by Avogadro’s number (number of atoms in 1 mole). And air seems to fit this rather well, as I understands it, even though being a mix.

Take a look here

Ideal gas. Is that a home work question? Or is it a serious idea, kind of unusual if so

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And a "mole is defined as the amount of substance that contains as many elementary entities (e.g., atoms, molecules, ions, electrons) as there are atoms in 12 g of the isotope carbon-12. Thus, by definition, one mole of pure 12C has a mass of exactly 12 g.

The experimentally determined value of a mole as adopted by CODATA in 2006 is 6.02214179(30)×1023

By this definition, a mole of any pure substance has a mass in grams exactly equal to that substance's molecular or atomic mass; e.g., 1mol of calcium-40 has an approximative mass of 40g, because the Ca-40 isotope has a mass of 39.9625906 amu on the C-12 scale. In other words, the numerical value of a substance's molecular or atomic mass in atomic mass units is the same as that of its molar mass—the mass of one mole of that substance—in grams.

The most common method of determining the amount, expressed in moles, of pure substance the value of whose molar mass is known, is to measure its mass in grams and then to divide by its molar mass (expressed in g/mol).[8] Molar masses may be easily calculated from tabulated values of atomic weights and the molar mass constant (which has a convenient defined value of 1 g/mol). Other methods include the use of the molar volume or the measurement of electric charge."